15 men can finish a job in 16 days. All the men work at the same rate.
Consider the following statements:
I. 20 men can finish the job in 12 days.
II. 12 men can finish the job in 18 days.
III. To finish the job in 10 days, 24 men are needed.
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → I and III only
For the same job, men \(\times\) days stays the same. Here the job needs \(15\times16=240\) man-days.
I. 20 men can finish the job in 12 days. — Correct. \(20\times12=240\) man-days.
Days \(=\displaystyle\frac{240}{20}=12\)
II. 12 men can finish the job in 18 days. — Incorrect. \(12\times18=216\) man-days is not enough; 12 men need 20 days.
Days \(=\displaystyle\frac{240}{12}=20\)
III. To finish the job in 10 days, 24 men are needed. — Correct. \(24\times10=240\) man-days.
Men \(=\displaystyle\frac{240}{10}=24\)